We generalize the convolution formula for the Tutte polynomial of Kook-Reiner-Stanton and Etienne-Las Vergnas to a more general setting that includes both arithmetic matroids and delta-matroids. As corollaries, we obtain new proofs of two positivity results for pseudo-arithmetic matroids and a combinatorial interpretation of the arithmetic Tutte polynomial at infinitely many points in terms of arithmetic flows and colorings. We also exhibit connections with a decomposition of Dahmen-Micchelli spaces and lattice point counting in zonotopes. Subsequently, we investigate the following problem: given a representable arithmetic matroid, when is the arithmetic matroid obtained by taking the kth power of its multiplicity function again representable? Bajo-Burdick-Chmutov have recently discovered that Arithmetic matroids of this type arise in the study of CW complexes. We also solve a related problem for the Grassmannian.